Kane scored the only goal of the game in the 59th minute at White Hart Lane before turning his ankle while attempting a sliding tackle on Papy Djilobodji.
He left the stadium on crutches, with his right foot in a protective boot.
Mousa Dembele and Eric Dier also came off with knocks in the second half, but Spurs boss Mauricio Pochettino said their injuries were not serious.
"I don't think Mousa and Eric will be a big issue, not big problems, I think they will be available for Middlesbrough [on 24 September]," he told Tottenham's official website.
"Harry Kane, we need to assess him tomorrow, it was a tough twist of his ankle and we'll have a scan and see."
Kane, Dier and Dembele could be doubts for Tottenham's League Cup third-round clash against Gillingham on 21 September.
'Pleased with response'
Pochettino said he was happy with the way his players bounced back after the disappointing 2-1 defeat against Monaco at Wembley in the Champions League.
"This is the way we want to see the team play," he said.
"It's not always about the result, it's about showing energy, performance, trying to win, to battle, to fight in every action and for that, I'm very happy.
"The players were all agreed after Wembley that we needed to show another way, to be more aggressive and show more passion.
"We were fantastic. In the end, it was only 1-0 after we created a lot of chances but I'm happy with the three points and now we look forward to the next game against Gillingham."
Spurs are one of only three teams to maintain an unbeaten record in the league this season. They lie in third place on the Premier League table, four points behind leaders Manchester City.